FIELD
[0001] The present disclosure relates to optical fibers, and in particular relates to a
quasi-single-mode optical fiber with a large effective area.
[0002] Prior art useful for understanding the present invention includes the publication
by
I. Roudas, et al., "Comparison of analytical models for the nonlinear noise in dispersive
coherent optical communications systems," IEEE Photonics Conference, paper MG3.4,
Bellevue, WA, Sept. 2013; the publication by
Sui et al., "256 Gb/s PM-16-QAM Quasi-Single-Mode Transmission over 2600 km using
Few-Mode Fiber with Multi-Path Interference Compensation," OFC Conference, San Francisco,
CA, March 9-13, 2014, Fiber Non-linearity Mitigation and Compensation (M3C) (ISBN:
978-1-55752-993-0); and the publication by
S.J. Savory, "Digital filters for coherent optical receivers," Optics Express, Vol.
16, No. 2, January 21, 2008, pp. 804-818.
BACKGROUND
[0003] Optical fibers are used for a variety of applications, especially in long-haul, highspeed
optical communications systems. Optical fibers have an optical waveguide structure
that acts to confine light to within a central region of the fiber. One of the many
benefits of optical fibers is their ability to carry a large number of optical signals
in different channels, which provides for high data transmission rates and a large
bandwidth.
[0004] The increasing demand for bandwidth and higher data transmission rates has resulted
in optical fibers carrying more channels and higher amounts of optical power. At some
point, however, the optical power carried by the optical fiber can give rise to non-linear
effects that distort the optical signals and reduce the transmission capacity of the
optical communications system. Consequently, there is a practical limit to how much
optical power an optical fiber can carry.
[0005] Because the optical power is confined by the waveguide structure of the optical fiber,
the intensity determines the severity of non-linear effects in the optical fiber.
The intensity is defined as the amount of optical power in the guided light divided
by the (cross-sectional) area over which the guided light is distributed. This area
is referred to in the art as the "effective area"
Aeff of the optical fiber. The effective area
Aeff is calculated from the electromagnetic field distribution of the light traveling
within the optical fiber using techniques and methods known in the art.
[0006] It is well-known that optical fibers with large effective areas
Aeff are desirable in optical transmission systems because of their relatively high power
threshold for nonlinear distortion impairments. The larger the effective area
Aeff, the lower the intensity and thus the less non-linear effects. Because of this feature,
an optical fiber with a large effective area
Aeff may be operated at higher optical powers, thereby increasing the optical signal-to-noise
ratio (OSNR).
[0007] Unfortunately, the effective area
Aeff of optical fibers cannot simply be increased without bound. The conventional wisdom
in the art is that an effective area
Aeff of about 150 µm
2 is the limit for a true single-mode fiber to maintain sufficient bend robustness,
(i.e., reduced loss due to bending). In some cases, an effective area
Aeff of 150 µm
2 may in fact already be too large for some bending-loss requirements. However, the
bending loss of an optical fiber can be reduced by increasing the mode confinement
and hence the cutoff wavelength of the optical fiber associated with single-mode operation.
Increasing the effective area
Aeff beyond present-day values would require raising the cutoff wavelength to be above
the signal wavelength, thereby resulting in few-mode operation, which gives rise to
undesirable optical transmission impairments such as modal dispersion and multipath
interference (MPI).
[0008] Alternatives to increasing the effective area
Aeff of the optical fiber to reduce adverse non-linear effects include decreasing the
effective nonlinear index
n2. The nonlinear physics of an optical fiber depends on the ratio
n2/
Aeff. However, changing
n2 is difficult and the resulting effect is likely to be very small. Reducing the fiber
attenuation is another alternative for better transmission performance. A lower fiber
attenuation reduces the need for amplification and thus reduces the noise of the transmission
link, which in turn reduces the required signal power for a given required OSNR. However,
reducing the attenuation of the optical fiber impacts the optical fiber transmission
system in a different way than by changing the effective area
Aeff, so that these two parameters cannot be exactly traded off.
[0009] What is needed therefore is a more robust type of large-effective-area optical fiber
that reduces adverse non-linear effects while also having sufficiently small bending
loss.
[0010] US 2004/114892 discloses an effective single mode optical fiber in which the cladding has a refractive
index that increases radially in the outward direction.
SUMMARY
[0012] An aspect of the disclosure is a QSM optical fiber according to claim 1.
[0013] In one example of the QSM fiber described above, the effective area
Aff > 200 µm
2 at 1530 nm.
[0014] Another aspect of the disclosure is a QSM optical fiber that has
n0 >
n1 >
n2 >
n3 and
nR >
n2>
n3.
[0015] In one example of the QSM fiber described immediately above, the effective area
Aeff > 200 µm
2. In another example,
n1 >
nR, while in other examples
n1 =
nR and
n1 <
nR.
[0016] Another aspect of the disclosure is an optical transmission system that includes
the QSM optical fiber as disclosed herein. The optical transmission system further
includes an optical transmitter configured to emit light that defines an optical signal
that carries information; an optical receiver optically coupled to the optical transmitter
by the QSM fiber and configured to receive the light emitted by the optical transmitter
and transmitted over the QSM optical fiber in the fundamental mode LP
01 and the higher-order mode LP
11 thereby giving rise to multipath interference (MPI), wherein the optical receiver
generates an analog electrical signal from the received light; an analog-to-digital
converter (ADC) that converts the analog electrical signal into a corresponding digital
electrical signal; and a digital signal processor electrically connected to the ADC
and configured to receive and process the digital electrical signal to mitigate the
MPI and generate a processed digital signal representative of the optical signal from
the optical transmitter.
[0017] Additional features and advantages are set forth in the Detailed Description that
follows, and in part will be readily apparent to those skilled in the art from the
description or recognized by practicing the embodiments as described in the written
description and claims hereof, as well as the appended drawings. It is to be understood
that both the foregoing general description and the following Detailed Description
are merely exemplary, and are intended to provide an overview or framework to understand
the nature and character of the claims.
BRIEF DESCRIPTION OF THE DRAWINGS
[0018] The accompanying drawings are included to provide a further understanding, and are
incorporated in and constitute a part of this specification. The drawings illustrate
one or more embodiment(s), and together with the Detailed Description serve to explain
principles and operation of the various embodiments. As such, the disclosure will
become more fully understood from the following Detailed Description, taken in conjunction
with the accompanying Figures, in which:
FIG. 1 is a front elevated view of a section of quasi-single-mode (QSM) fiber as disclosed
herein;
FIG. 2 is a plot of the refractive index n versus radius r that illustrates an example refractive index profile for an example of the QSM fiber
of FIG. 1;
FIG. 3 is similar to FIG. 2 and illustrates an example refractive index profile for
the QSM fiber that does not include the ring portion of the cladding section, and
which is not part of the present invention;
FIG. 4 is a close-up, cross-sectional view of the QSM fiber of FIG. 1, illustrating
an example where the fiber includes an axial (longitudinal) refractive-index perturbation
designed to provide substantial attenuation of the higher-order mode while not substantially
attenuating the fundamental mode;
FIG. 5 is similar to FIG. 2 and illustrates in a single plot three different refractive
index profiles p1, p2 and p3 for example QSM fibers, wherein the inner cladding for
the different profiles has different depths;
FIG. 6 is a plot of the bending loss BL (dB/turn) versus the bending diameter DB (mm) for the three refractive index profiles p1, p2 and p3 of FIG. 5;
FIG. 7 is a plot of the ratio of the measured outputted optical power POUT to the inputted optical power PIN (POUT/PIN) versus the wavelength λ (nm) for the three different refractive index profiles p1,
p2 and p3 of FIG. 5, wherein the plot is used to calculate the cutoff wavelength λc from multimode to single-mode operation;
FIGS. 8A and 8B plot of the signal power distribution SP in arbitrary power units
(a.p.u.) as a function of the differential mode delay or DMD (ns) in a two-mode (LP01 and LP11) QSM optical fiber for the case where there is negligible mean differential modal
attenuation or DMA (FIG. 8A) and for the case where there is a high DMA (FIG. 8B),
wherein the solid shows the total power, the dashed line shows the power in the fundamental
mode LP01, and the dashed-dotted line shows the power in the higher-order mode LP11;
FIGS. 9A and 9B are plots of the effective DMD, denoted DMDEff, versus the DMA (dB/km) for an example optical transmission system that employs an
example of the QSM fiber disclosed herein, wherein for FIG. 9A the DMD units are nanoseconds
whereas in FIG. 9B the DMDEff is in units of the tap (temporal) spacing τ of the signal processor; and
FIG. 10 is a schematic diagram of an optical transmission system that employs the
QSM fiber as disclosed herein along with MPI compensation to recover the signal that
travels in the fundamental LP01 mode of the QSM fiber.
DETAILED DESCRIPTION
[0019] Reference is now made in detail to various embodiments of the disclosure, examples
of which are illustrated in the accompanying drawings. Whenever possible, the same
or like reference numbers and symbols are used throughout the drawings to refer to
the same or like parts. The drawings are not necessarily to scale, and one skilled
in the art will recognize where the drawings have been simplified to illustrate the
key aspects of the disclosure.
[0020] The claims as set forth below are incorporated into and constitute part of this Detailed
Description.
Terminology
[0021] The term "relative refractive index," as used herein in connection with the multimode
fibers and fiber cores discussed below, is defined as:
where n(r) is the refractive index at radius
r, unless otherwise specified and
nS is the reference index. The relative refractive index is defined at the operating
wavelength
λp. In another aspect,
nS is the index of undoped silica (SiO
2). The maximum index of the index profile is denoted
n0, and in most cases,
n0 =
n(0).
[0022] As used herein, the relative refractive index is represented by Δ and its values
are given in units of "%," unless otherwise specified. In the discussion below, the
reference index
nREF is that for pure silica.
[0023] The term "dopant" as used herein generally refers to a substance that changes the
relative refractive index of glass relative to pure (undoped) SiO
2 unless otherwise indicated.
[0024] The term "mode" is short for a guided mode or optical mode. A "multimode" optical
fiber means an optical fiber designed to support the fundamental guided mode and at
least one higher-order guided mode over a substantial length of the optical fiber,
such as 2 meters or longer. A "single-mode" optical fiber is an optical fiber designed
to support a fundamental guided mode only over a substantial length of the optical
fiber, such as 2 meters or longer. A "few mode" or "few-moded" optical fiber is an
optical fiber designed to support a fundamental guided mode and one or two higher-order
modes over a substantial length of the optical fiber, such as 2 meters or longer.
A "quasi-single mode" fiber is distinguished from a "few-mode" fiber in that the former
seeks to use only the fundamental mode to carry information while the latter seeks
to use all of the few modes to carry information.
[0025] The term "cutoff' is used herein refers to the cutoff wavelength λ
c that defines the boundary for single-mode and multimode operation of an optical fiber,
wherein single-mode operation of the fiber occurs for wavelengths λ > λ
c. The cutoff wavelength λ
c as the term is used herein can be measured by the standard 2 m fiber cutoff test,
FOTP-80 (EIA--TIA-455-80), to yield the "fiber cutoff wavelength," also known as the
"2 m fiber cutoff" or "measured cutoff". The FOTP-80 standard test is performed to
either strip out the higher order modes using a controlled amount of bending, or to
normalize the spectral response of the fiber to that of a multimode fiber.
[0026] For examples of the QSM fiber disclosed herein, the cutoff wavelength λ
c > 1600 nm, or more preferably λ
c > 1700 nm, or more preferably λ
c > 1750 nm, or even more preferably λ
c > 1800 nm.
[0027] The number of propagating modes and their characteristics in a cylindrically symmetric
optical fiber with an arbitrary refractive index profile is obtained by solving the
scalar wave equation (see for example T.A. Lenahan, "Calculation of modes in an optical
fiber using a finite element method and EISPACK," Bell Syst. Tech. J., vol. 62,no.
1, p. 2663, Feb. 1983). The light traveling in an optical fiber is usually described
(approximately) in terms of combinations of LP (linear polarization) modes. The LP
0p modes with p>0 have two polarization degrees of freedom and are two-fold degenerate.
The LP
mp modes with m > 0, p>0 have both two polarization and two spatial degrees of freedom.
They are four-fold degenerate. In the discussion herein, polarization degeneracies
are not counted when designating the number of LP modes propagating in the fiber.
For example, an optical fiber in which only the LP
01 mode propagates is a single-mode fiber, even though the LP
01 mode has two possible polarizations. A few-mode (or "few moded") optical fiber in
which the L
01 and LP
11 modes propagate supports three spatial modes but nevertheless is referred herein
as having two modes for ease of discussion.
[0028] As used herein, the "effective area"
Aeff of an optical fiber is the cross-sectional area of the optical fiber through which
light is propagated and is defined as:
where
E is the electric field associated with light propagated in the fiber and
r is the radius of the fiber. The effective area
Aeff is determined at a wavelength of 1550 nm, unless otherwise specified.
[0029] Macrobend performance of the example QSM fibers disclosed herein was determined according
to FOTP-62 (IEC-60793-1-47) by wrapping 2 turns around a mandrel having a diameter
D
B (e.g., D
B = 60 mm) and measuring the increase in attenuation due to the bending using an encircled
flux (EF) launch condition.
[0030] In the discussion below, any portion of the optical fiber that is not the core is
considered part of the cladding, which can have multiple sections. In some of the
Figures (e.g., FIG. 1 and FIG. 4), the cladding is shown has having a limited radial
extent (e.g., out to radius
rg) for ease of illustration even though the cladding in principle extends beyond this
limit.
[0031] The C-band is defined as the wavelength range from 1530 nm to 1565 nm; The L-band
is defined as the wavelength range from 1565 nm to 1625 nm; and the C+L wavelength
band is defined as the wavelength range from 1530 nm to 1625 nm.
[0032] The limits on any ranges cited herein are considered to be inclusive and thus to
lie within the stated range, unless otherwise specified.
QSM optical fiber
[0033] FIG. 1 is an elevated view of a section of a QSM fiber 10 as disclosed herein. The
QSM fiber 10 has a body 11 configured as described below and includes a centerline
12 that runs longitudinally down the center of the QSM fiber.
[0034] FIG. 2 is a plot of the refractive index
n versus radius
r of QSM fiber 10 as measured from centerline 12, illustrating an example refractive
index configuration (profile) for the QSM fiber. The QSM fiber 10 has a central core
("core") 20 with a cladding section 30 surrounding the core. In an example, core 20
is made primarily silica and preferably alkali doped, e.g., potassium doped silica.
Core 20 is preferably substantially free, and preferably entirely free, of GeO
2. Core 20 may also include fluorine as a dopant.
[0035] The cladding section 30 includes a number of regions, namely a first inner annular
cladding region or "inner cladding" 32, a second inner annular cladding region or
"moat" 34 surrounding the inner cladding, and an annular outer cladding region or
"ring"38 surrounding moat 34. The shape of the core 20 is approximately triangular,
but can vary from a step profile to an alpha profile. The core 20 has an outer edge
21 at a radius
re, which can be considered the core radius, which in example is also equal to radius
r1. In one example, the core radius
re or
r1 > 5 µm, while in another example,
re or
r1 > 7 µm.
[0036] In an example, neither the core 20 nor the cladding section 30 includes germanium.
The different regions of cladding section 30 may be made of fluorine-doped silica.
In an example, cladding section 30 is doped with fluorine while core 20 is doped with
potassium.
[0037] The example refractive index profile of the example QSM fiber 10 of FIG. 2 can be
described by nine fiber parameters (P): Five refractive indices
n0, n1, n2, n3 and
nR, and four radii
r1, r2, r3 and
rR. The refractive index
n0 is the peak refractive index and occurs at
r = 0, i.e., on centerline 12 within core 20. The refractive index
n1 represents the refractive index at the interface between the core 20 and the adjacent
inner cladding 32, i.e., at the core edge 21, which in an example is associated with
radius
re. The refractive index
n2 represents the minimum refractive index for inner cladding 32. The refractive index
n3 represents the minimum refractive index for moat 34. The refractive index
nR represents the refractive index of ring 38.
[0038] In an example, the radius
r1 represents both the radius of core 20 and the inner radius of inner cladding 32,
while the radius
r2 represents the outer radius of the inner cladding. The radius
r3 represents the outer radius of moat 34. The radius
rR represents the inner radius of ring 38. The radius
rg represents the radius where ring 38 ends and the glass coating 39 of refractive index
ng that makes up the rest of the QSM fiber 10 begins.
[0039] In an example, the nine fiber parameters P are designed for a nominal glass radius
rg = 62.5 µm. Small adjustments, to especially the cladding parameters (
r3, n3) and ring parameters (
nR, rR) may be required if the fiber glass radius
rg is changed, which is optional for reducing bending loss. In FIG. 1, the core edge
radius
re is slightly smaller than the inner cladding radius
r1 due to shortcomings in the refractive index measurement. In the plot of FIG. 5 discussed
below, the transition from core 20 to inner cladding 32 is vertical so that
re =
r1.
[0040] In an example embodiment of QSM fiber 10,
n0 > n1 > n3 > n2. In another example,
n1 >
nR, while another example
n1 ≤ nR. Also in an example,
nR > n3 > n2.
[0041] FIG. 3 is similar to FIG. 2 and illustrates an example refractive index profile for
an example QSM fiber 10 not part of the present invention wherein the cladding region
30 does not include the outer ring 38. For the "no-ring" profile of FIG. 3, the inner
radius of inner cladding 32 is denoted
ri and has an associated refractive index
ni. The shape of the core 20 is approximately step-like in the example, but can vary
from a step profile to an alpha profile. The small bumps bi and b2 in the refractive
index profile of FIG. 3 are features arising from the expected draw stress distribution
and are not critical to the design. As noted above, the inner radius
ri of inner cladding 32 can be equal to the radius
r1 of core 20.
[0042] The QSM fiber 10 disclosed herein has a relatively large effective area
Aeff, which in one example is
Aeff > 150 µm
2, while in another example is
Aeff > 170 µm
2, while yet in another example is
Aeff > 200 µm
2. The QSM fiber 10 is designed to be operated using only the fundamental mode LP
01 just as in single-mode fiber, while the one additional higher-order mode LP
11 is not used. The one additional higher-order mode LP
11 can impair the transmission of optical signals traveling in the QSM fiber unless
appropriate MP-compensating digital signal processing is applied to the received (transmitted)
signal.
[0043] In an example, the fundamental mode LP
01 has a fundamental-mode effective index, the higher-order mode LP
11 has a higher-order-mode effective index, and wherein a difference Δ
neff between the fundamental-mode effective index and the higher-order-mode effective
index is |Δ
neff| > 0.001 at a wavelength of 1550 nm.
Higher-order-mode impairments
[0044] The main two impairments caused by the presence of the higher-order mode LP
11 in QSM fiber 10 are multipath interference (MPI) and excess loss (EL). An aspect
of the disclosure includes using QSM fiber 10 for optical signal transmission while
electronically mitigating MPI of the optical signal using digital signal processing
techniques that are known in the art and as described in greater detail. The electronic
mitigation of MPI effects enables the deployment of QSM fiber 10 in an optical transmission
system. To this end, in an example, the aforementioned parameters P of QSM fiber 10
are substantially optimized, while the excess loss EL, which cannot be compensated,
is substantially minimized (e.g., made substantially zero). This avoids having the
excess loss EL reduce the benefit of having a relatively large effective area
Aeff used to overcome detrimental non-linear effects, as explained above.
[0045] Because the higher-order mode LP
11 of QSM fiber 10 is undesirable and unused, the design and configuration of QSM fiber
10 is different than that for conventional few-mode optical fibers that seek to transmit
information in the higher-order modes. In particular, because conventional few-mode
optical fibers seek to utilize the information transmitted in the few higher-order
modes, these modes need to have relatively low differential modal attenuation (DMA).
As is explained in greater detail below, the QSM fiber 10 disclosed herein has relatively
high DMA, i.e., the higher-order mode LP
11 is intentionally subjected to a relatively large attenuation to reduce the degree
of optical transmission impairment caused by this higher-order mode.
[0046] Ideally, QSM fiber 10 would have a relatively large phase index difference between
all supported modes to minimize mode-coupling, while at the same time having a small
group index difference between all supported modes. This latter attribute minimizes
the digital signal processing required to remove MPI artifacts from the received signal.
Unfortunately, this is not possible in fibers with large effective area
Aeff. Qualitatively, this is because, for any mode, the group index (
ng) is related to phase index (or "effective index"
ne) as follows:
The difference in the group index
ng between two modes is therefore given by:
[0047] In the limit of very large effective area
Aeff, the wavelength dispersion of all modes approaches that of the bulk glass, in which
case the last term in the equation for Δ
ng vanishes so that Δ
ng ≈ Δ
ne. Consequently, one cannot simultaneously have a low mode coupling (large Δ
ne) and a small differential mode delay (DMD, small Δ
ng).
[0048] In the QSM fiber 10 disclosed herein, low mode coupling is substantially preserved
while, as noted above, the DMD is managed by intentionally designing the QSM fiber
to have as much loss (i.e., a high DMA) as possible for the higher-order mode LP
11. A high DMA reduces the number of equalizer taps (i.e., memory) required in the digital
signal processor used for MPI compensation, thereby reducing system complexity, as
described below. High DMA values also reduce the total MPI level, which may have an
upper limit in terms of the efficacy of the MPI compensation digital signal processing.
[0049] In one example, the DMA for a wavelength of 1530 nm is DMA ≥ 1.0 dB/km, while in
another example, the DMA ≥ 4.0 dB/km. Also in one example, the coupling coefficient
CC between the fundamental mode LP
01 and the higher-order mode LP
11 at a wavelength of 1530 nm is CC < 0.002 km
-1, while in another example, the coupling coefficient CC < 0.001 km
-1.
[0050] One way to increase the DMA for the higher-order mode LP
11 is to shift the cutoff wavelength λ
c to its lowest possible value consistent with macrobend requirements. Another way
is to make the higher-order modes lossy in a mode-selective way. FIG. 4 is a close-up
cross-sectional view of a portion of an example QSM fiber 10 that includes an axial
(longitudinal) refractive-index perturbation 52. FIG. 4 includes a plot of refractive
index
n versus the axial distance z down the QSM fiber that illustrates an example form of
the refractive-index perturbation having a constant period A. The refractive-index
perturbation 52 is configured to increase the attenuation (DMA) of the higher-order
mode LP
11 while not substantially increasing the attenuation of the fundamental mode LP
01. In an example, refractive-index perturbation 52 is in the form of a long-period
grating that substantially matches a difference in the effective indices of the higher-order
mode LP
11 and a radiative cladding mode at the operating wavelength, i.e., a period Λ ≈ 1/Δ
n, where Δ
n is the effective index difference between the higher-order mode LP
11 and the radiative cladding mode).
[0051] In an example, axial refractive-index perturbation 52 has a wavelength resonance
and includes a non-constant (e.g., chirped) period A that serves to to widen the bandwidth
of the resonance as compared to the constant period configuration. In an example,
axial refractive-index perturbation 52 can be formed in QSM fiber 10 using known methods,
such as laser irradiation. In an example, the axial refractive-index perturbation
52 can be formed as the fiber is being drawn, such as by irradiating the fiber with
one or more lasers. In an example, the period A of the refractive-index perturbation
is chosen such that there is substantially no resonant coupling of the LP
01 and LP
11 modes in the C+L bands, and in an example at a wavelength of 1530 nm.
[0052] The so-called "Gaussian Noise (GN)" model of optical transmission posits that the
launch-power-optimized system Q-factor scales with the effective area
Aeff as:
so that increasing the effective area
Aeff from 150 to 175 µm
2 increases
Q2 by about 11% or 0.45 dB. Increasing the effective area
Aeff from 150 to 250 µm
2 increases
Q2 by 41% or 1.5 dB. An example simulation was carried out for an erbium-doped fiber-amplified
(EDFA) polarization-multiplexed (PM)-16QAM (Quadrature Amplitude Modulation) optical
transmission system having 80 channels, a 32 GHz (Nyquist) channel spacing, a 50 km
span length, ideal (noise and distortion-free) transmitter and receivers and a QSM
fiber 10 with span loss of 0.158 dB/km. The simulation shows that increasing the effective
area
Aeff from 150 µm
2 to 250 µm
2 increases the reach at 11.25 dB from 3000 km to 4000 km. Hence, while a 1.5 dB increase
in optimal
Q2 seems small, it can lead to a significant reach improvement.
[0053] This simulation suggests that with 50 km spans, increasing the effective area
Aeff from 150 µm
2 to 250 µm
2 and increasing the span loss from 0.158 dB/km to 0.215 dB/km produces no net change
in
Q2. Hence the excess loss EL (i.e., the additional loss resulting from mode coupling
above the intrinsic LP
01 attenuation) of just 0.057 dB/km can completely erase the advantage of the increase
in effective area
Aeff. An excess loss EL of even 0.01 dB/km can decrease the reach of QSM fiber 10 with
an effective area
Aeff = 250 µm
2 by about 200 km. The advantage of large effective area fibers with an effective area
Aeff of less than 250 µm
2 would likewise be reduced.
[0054] It was found through modeling that conventional refractive index profiles cannot
achieve sufficiently large DMA and effective areas
Aeff exceeding 175 µm
2 without also introducing excess macrobend loss. However, it was also found that the
judicious addition of the ring 38 of increased refractive index
nR relative to the refractive index
nc of the outer cladding 34 can enhance the LP
11 mode coupling to the glass coating 39, thereby increasing the DMA without significantly
impacting bend performance. In this regard, the index
nR of the ring 38 must not exceed the effective index
neff of the fundamental mode. In an example, ring 38 includes at least one absorbing dopant
that contribute to the attenuation of the higher-order mode LP
11. Examples of absorbing dopants include titanium or other transition metals. In another
example, ring 38 does not include any absorbing dopants. In an example, ring 38 includes
fluorine dopant, which is not an absorbing dopant.
Example QSM fibers
[0055] Table 1 below sets forth example QSM fiber parameters P for three examples of QSM
fiber 10. In the Tables below, P stands for the given parameter, "MINI" and "MAX1"
stand for first example minimum and maximum values for the given parameter, "MIN2"
and "MAX2" for second example minimum and maximum values for the given parameter,
and "MIN3" and "MAX3" for third example minimum and maximum values for the given parameter.
The parameters P in the following Tables are based on QSM fiber 10 having a nominal
radius
rg = 62.5 µm.
TABLE 1 - EXAMPLE 1 |
P |
MIN0 |
MAX0 |
MIN1 |
MAX1 |
MIN2 |
MAX2 |
n0 |
1.4430 |
1.4450 |
1.4436 |
1.4448 |
1.4438 |
1.4447 |
n1 |
1.4430 |
1.4450 |
1.4430 |
1.4436 |
1.4432 |
1.4434 |
n2 |
1.4400 |
1.4430 |
1.4406 |
1.4419 |
1.4408 |
1.4415 |
n3 |
1.4390 |
1.4430 |
1.4406 |
1.4422 |
1.4408 |
1.4412 |
r1 [µm] |
5 |
15 |
7 |
12 |
8 |
11 |
r2 [µm] |
25 |
38 |
28 |
35 |
31 |
33 |
r3 [µm] |
40 |
62.5 |
45 |
55 |
48 |
52 |
rR [µm] |
40 |
62.5 |
47 |
57 |
50 |
54 |
[0056] Table 2 below is an alternative representation of the refractive index data of Table
1. In Table 2, the refractive index change relative to pure silica is used. This refractive
index change is represented by the relative refractive index Δ, which is given by
where
n is the refractive index value from the tables above (at 1550 nm) and
nS = 1.444374, the refractive index of pure silica.
TABLE 2 - EXAMPLE 1 USING Δ VALUES |
P |
MIN |
MAX |
MIN1 |
MAX1 |
MIN2 |
MAX2 |
Δ0 |
-9.5082E-04 |
4.3350E-04 |
-5.3573E-04 |
2.9498E-04 |
-3.9733E-04 |
2.2573E-04 |
Δ1 |
-9.5082E-04 |
4.3350E-04 |
-9.5082E-04 |
-5.3573E-04 |
-8.1248E-04 |
-6.7411E-04 |
Δ2 |
-3.0237E-03 |
-9.5082E-04 |
-2.6095E-03 |
-1.7114E-03 |
-2.4714E-03 |
-1.9878E-03 |
Δ3 |
-3.7137E-03 |
-9.5082E-04 |
-2.6095E-03 |
-1.5040E-03 |
-2.4714E-03 |
-2.1951E-03 |
r1 [µm] |
5 |
15 |
7 |
12 |
8 |
11 |
R2 [µm] |
25 |
38 |
28 |
35 |
31 |
33 |
r3 [µm] |
40 |
62.5 |
45 |
55 |
48 |
52 |
rR [µm] |
40 |
62.5 |
47 |
57 |
50 |
54 |
[0057] Another example of QSM fiber 10 not being part of the invention is set forth in Table
3 below and represents an example of the "no ring" configuration such as shown in
FIG. 3.
TABLE 3 - EXAMPLE (NO RING) |
P |
MIN |
MAX |
MIN1 |
MAX1 |
MIN2 |
MAX2 |
n0 |
1.4435 |
1.4445 |
1.4437 |
1.4443 |
1.4438 |
1.4442 |
n1 |
1.4430 |
1.4450 |
1.4427 |
1.4438 |
1.4430 |
1.4435 |
ni |
1.4410 |
1.4420 |
1.4412 |
1.4418 |
1.4413 |
1.4417 |
n2 |
1.4397 |
1.4413 |
1.4400 |
1.4412 |
1.4402 |
1.4409 |
n3 |
1.4380 |
1.4410 |
1.4387 |
1.4405 |
1.4390 |
1.4402 |
r1 [µm] |
5 |
12 |
5 |
10 |
6 |
9 |
ri [µm] |
6 |
13 |
7 |
12 |
7 |
11 |
r2 [µm] |
18 |
33 |
19 |
29 |
20 |
25 |
[0058] Another example of QSM fiber 10 not being part of the invention is set forth in Table
4 below and represents another example of the "no ring" configuration.
TABLE 4 - EXAMPLE 3 (NO RING) |
P |
MIN |
MAX |
MIN1 |
MAX1 |
MIN2 |
MAX2 |
n0 |
1.4435 |
1.4445 |
1.4437 |
1.4443 |
1.4438 |
1.4442 |
n1 |
1.4425 |
1.4435 |
1.4426 |
1.4433 |
1.4427 |
1.4432 |
ni |
1.4410 |
1.4420 |
1.4412 |
1.4418 |
1.4405 |
1.4409 |
n2 |
1.4397 |
1.4413 |
1.4400 |
1.4412 |
1.4402 |
1.4409 |
n3 |
1.4380 |
1.4410 |
1.4387 |
1.4405 |
1.4390 |
1.4402 |
r1 [µm] |
6 |
14 |
6 |
12 |
7 |
10 |
ri [µm] |
7 |
15 |
8 |
14 |
9 |
13 |
r2 [µm] |
25 |
35 |
20 |
34 |
25 |
30 |
QSM properties of example profiles
[0059] FIG. 5 is similar to FIG. 2 and shows first, second and third example refractive
index profiles p1, p2 and p3 (solid, dashed and dotted lines, respectively) for example
QSM fibers 10, wherein the different index profiles have different depths for inner
cladding 32. FIG. 6 is a plot of the predicted bend loss BL (dB/turn) versus bend
diameter D
B (mm) at a wavelength of 1625 nm as obtained using optical modeling. The three solid
straight lines in FIG. 5 are approximate upper bounds for the example profiles p1,
p2 and p3 based on fitting the oscillation peaks. All three example profiles p1, p2
and p3 yield a bending loss BL < 5 mdB/turn at a bend diameter D
B of 60 mm.
[0060] FIG. 7 is a plot of the ratio of the measured outputted optical power P
OUT to the inputted optical power P
IN (P
OUT/P
IN) versus the wavelength λ (nm) for the three different refractive index profiles p1,
p2 and p3 of FIG. 5, wherein the plot is used to calculate the cutoff wavelength λ
c from multimode to single-mode operation.
[0061] Table 5 below summarizes the predicted optical properties of the three example profiles
p1, p2 and p3 of FIG. 5. The values for the bending loss BL are obtained from the
straight-line fits of FIG. 6 while the cut-off wavelengths λ
c are estimated from the power trace plots of FIG. 7. The effective area
Aeff is measured in µm
2 at λ = 1550 nm. The straight fiber LP
11 mode cutoff wavelength λ
c is measured in nanometers (nm). The straight-fiber LP
11 mode radiative loss at 1550 nm is denoted RL and is measured in dB/km. The fundamental
mode macro-bend loss BL is measured in dB/turn at λ = 1625 nm and a bend diameter
D
B = 60 mm.
TABLE 5 - PREDICTED OPTICAL PROPERTIES FOR 3 EXAMPLE PROFILES |
Profile |
Aeff [µm2] |
λc [nm] |
RL [dB/km] |
BL [dB/turn] |
p1 |
237 |
1800 |
11.4 |
1.9x10-3 |
p2 |
232 |
1850 |
5.1 |
0.9x10-3 |
p3 |
227 |
1885 |
2.3 |
0.6x10-3 |
Relationship between DMA and NT
[0062] One of the advantages of QSM fiber 10 is that it reduces the number of taps needed
for the digital signal processor used for MPI compensation in an optical transmission
system. FIGS. 8A and 8B plot the signal power distribution SP in arbitrary power units
(a.p.u.) as a function of the DMD (ns) in a two-mode (LP
01 and LP
11) QSM fiber 10. The solid shows the total power; the dashed line shows the power in
the fundamental mode LP
01; the dashed-dotted line shows the power in the higher-order mode LP
11.
[0063] In FIG. 8A, there is negligible mean DMA, while in FIG. 8B here is a high mean DMA.
All other fiber parameters P were kept the same, and in both cases the signal was
launched into the fundamental mode LP
01 only. The amount of significantly delayed contributions (the tail of the dashed black
line) is decreased as the DMA increases. This enables use of a QSM fiber 10 having
a relatively large DMD with a digital signal processor having a reduced number N
T of taps as compared to conventional MPI compensation.
[0064] The amount of significantly delayed contributions (the tail of the dashed black line)
is decreased as the DMA increases. This enables use of a QSM fiber 10 having a relatively
large DMD with a digital signal processor having a reduced number N
T of taps as compared to conventional MPI compensation.
[0065] FIGS. 9A and 9B plot the effective DMD, denoted DMD
Eff, versus the DMA (dB/km) for an example optical transmission system that utilizes
the QSM fiber 10 disclosed herein. In FIG. 9A, the DMD
Eff has units of nanoseconds (ns) while in FIG. 9B the DMD
Eff is in units of the tap (temporal) spacing τ of the signal processor, wherein each
tap has duration of 31.25 ps. The effective DMD is defined as the time interval that
includes 99.95% of the interfering pulse energy and represents the amount of delay
the digital signal processor needs to compensate for MPI. The calculations used to
generate FIGS. 9A and 9B assume a DMD of 1 ns/km and a length L = 100 km of QSM fiber
10.
[0066] The plots of FIGS. 9A and 9B show the effect of the non-zero DMA on the number N
T of taps needed to compensate for the optical transmission impairment of the information-carrying
optical signal traveling in the fundamental mode. The calculation of the required
number N
T of equalizer taps is approximate. The calculation is based on a mean MPI compensation,
so the results can be considered as establishing a lower bound on the number N
T of taps.
Optical transmission system with QSM fiber
[0067] FIG. 10 is a schematic diagram of an example optical transmission system ("system")
100 that employs the QSM fiber 10 as disclosed herein. System 100 includes an optical
transmitter 110, a section of QSM fiber 10, an optical receiver 130, an analog-to-digital
converter ADC electrically connected to the optical receiver and a digital signal
processor DSP electrically connected to the analog-to-digital converter. Also optionally
included in system 100 is a decision circuit 150 electrically connected to the digital
signal processor DSP.
[0068] The digital signal processor DSP includes an MPI mitigation system 134 that in example
includes a plurality of equalizer taps 136. System 10 and in particular MPI mitigation
system 134 is configured to perform electronic equalization of optical transmission
impairments to the optical signal using methods known in the art. In one example,
MPI mitigation system 134 includes four finite impulse response (FIR) filters in a
butterfly structure (not shown), wherein each filter has a number of taps 136, which
are recursively adjusted based on a least-mean-square (LMS) algorithm.
[0069] The QSM fiber section 10 includes an input end 112 optically connected to optical
transmitter 110 and an output end 114 optically connected to optical receiver 130,
thereby establishing an optical connection between the optical transmitter and the
optical receiver. In an example, QSM fiber 10 includes an amplifier 160, e.g., an
EDFA.
[0070] In the operation of system 100, transmitter 110 generates light 200 that defines
an input analog optical signal OS that carries information only in the fundamental
mode LP
01. Light 200 enters the input end 112 of QSM fiber 10 and travels the length of the
fiber to output end 114. Most of light 200 travels in the fundamental mode (LP
01) while a portion of the light travels in the higher-order mode LP
11. The light 200 is denoted as 200' at the output end of QSM fiber 10 due the light
having impairments described above by virtue of having traveled through QSM fiber
10.
[0071] Optical receiver 130 receives light 200' as emitted from the output end 114 of QSM
fiber 10 and converts this light into a corresponding analog electrical signal SA.
The analog electrical signal SA passes through analog-to-digital converter ADC, which
forms therefrom a corresponding digital electrical signal SD. The digital electrical
signal SD is then received by digital signal processor DSP, which performs digital
processing of the digital electrical signal. In particular, the digital signal processor
DSP is configured to perform equalization of MPI using MPI mitigation system 134 and
the equalizer taps 136 therein based on techniques known in the art. The digital signal
processor DSP outputs a processed digital electrical signal SDP that is representative
(to within the limits of MPI mitigation system 134) of the initial optical signal
OS generated by transmitter 110. The processed digital electrical signal SDP, which
includes the information originally encoded into optical system OS, continues downstream
to be processed as needed (e.g., by a decision circuit 150) for the given application.
[0072] As noted above, the relatively high DMA of ≥ 1dB/km or > 4 dB/km results in less
complex digital signal processing, i.e., the number N
T of equalizer taps 136 is reduced as compared to conventional optical transmission
systems that employ MPI compensation. Also, as noted above, high DMA values also reduce
the total MPI level, which may have an upper limit in terms of the efficacy of the
MPI compensation digital signal processing.
[0073] It will be apparent to those skilled in the art that various modifications to the
preferred embodiments of the disclosure as described herein are possible, provided
they come within the scope of the appended claims.